Efficient Solution of Language Equations Using Partitioned Representations

A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix closed, and are naturally represented by multi-level networks with latches. For this special case, we present an efficient computation, using partitioned representations, of the most general prefix-closed solution of the above class of language equations. The transition and the output relations of the FSMs for F and S in their partitioned form are represented by the sets of output and next state functions of the corresponding networks. Experimentally, we show that using partitioned representations is much faster than using monolithic representations, as well as applicable to larger problem instances.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

On the Notion of Proposition in Classical and Quantum Mechanics

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language $L_{TQ}(x)$, and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.Comment: 22 pages. To appear in "The Foundations of Quantum Mechanics: Historical Analysis and Open Questions-Cesena 2004", C. Garola, A. Rossi and S. Sozzo Eds., World Scientific, Singapore, 200

Multiword expressions in an LFG grammar for Norwegian

This chapter describes the analysis of multiword expressions in NorGram, an LFG grammar of Norwegian. All multiword expressions need to be accounted for in the lexicon, but in different ways depending on the flexibility of the expression. Each multiword expression is provided with a lexical entry that has a special predicate name incorporating the lexical items that the multiword consists of and that specifies the argument structure of the predicate. In this way, analyses are provided for a wide range of multiword types, including fixed expressions, phrasal verbs, verbal idioms, and others.publishedVersio

The infinitive and the gerund-participle as complements of verbs of risk

Ce mémoire, puisant à même certains principes de la linguistique cognitive et de la psychomécanique du langage, porte sur la complémentation verbale de l'anglais avec l'infinitif et le gérondif. Par l'entremise d'un corpus de données attestées, nous expliquons les divers effets de sens et les principes qui sous-tendent l'usage des structures 'verbe principal + complément' avec l'infinitif et le gérondif comme compléments de verbes comportant une idée de risque, soit risk, venture, adventure, hazard, chance, dare, face, jeopardize, endanger et imperil. Plus particulièrement, les problèmes de temporalité et de contrôle sont examinés. Trois paramètres permettent d'expliquer les effets de sens 'et le contraste entre les structures à l'étude : 1) le sens grammatical du complément, 2) sa fonction en relation avec le verbe principal, et 3) le sens lexical du verbe principal. L'analyse des deux premiers paramètres est fondée sur les hypothèses proposées par Duffley (2000 ; 2006)

The Cook-Reckhow definition

The Cook-Reckhow 1979 paper defined the area of research we now call Proof Complexity. There were earlier papers which contributed to the subject as we understand it today, the most significant being Tseitin's 1968 paper, but none of them introduced general notions that would allow to make an explicit and universal link between lengths-of-proofs problems and computational complexity theory. In this note we shall highlight three particular definitions from the paper: of proof systems, p-simulations and the pigeonhole principle formula, and discuss their role in defining the field. We will also mention some related developments and open problems

Boundary Algebra: A Simpler Approach to Boolean Algebra and the Sentential Connectives

Boundary algebra [BA] is a algebra of type , and a simplified notation for Spencer-Brown’s (1969) primary algebra. The syntax of the primary arithmetic [PA] consists of two atoms, () and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting, indifferently, the presence or absence of () into a PA formula yields a BA formula. The BA axioms are A1: ()()= (), and A2: “(()) [abbreviated ‘⊥’] may be written or erased at will,” implying (⊥)=(). The repeated application of A1 and A2 simplifies any PA formula to either () or ⊥. The basis for BA is B1: abc=bca (concatenation commutes & associates); B2, ⊥a=a (BA has a lower bound, ⊥); B3, (a)a=() (BA is a complemented lattice); and B4, (ba)a=(b)a (implies that BA is a distributive lattice). BA has two intended models: (1) the Boolean algebra 2 with base set B={(),⊥}, such that () ⇔ 1 [dually 0], (a) ⇔ a′, and ab ⇔ a∪b [a∩b]; and (2) sentential logic, such that () ⇔ true [false], (a) ⇔ ~a, and ab ⇔ a∨b [a∧b]. BA is a self-dual notation, facilitates a calculational style of proof, and simplifies clausal reasoning and Quine’s truth value analysis. BA resembles C.S. Peirce’s graphical logic, the symbolic logics of Leibniz and W.E. Johnson, the 2 notation of Byrne (1946), and the Boolean term schemata of Quine (1982).Boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; G. Spencer-Brown; C.S. Peirce; existential graphs